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Asymptotic strictly pseudoconvex CR structure for asymptotically locally complex hyperbolic manifolds
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0001-6454-5016
2024 (English)In: Mathematische Zeitschrift, ISSN 0025-5874, E-ISSN 1432-1823, Vol. 307, no 1, article id 8Article in journal (Refereed) Published
Abstract [en]

In this paper, we build a compactification by a strictly pseudoconvex CR structure for a complete and non-compact Kähler manifold whose curvature tensor is asymptotic to that of the complex hyperbolic space. To do so, we study in depth the evolution of various geometric objects that are defined on the leaves of some foliation of the complement of a suitable convex subset, called an essential subset, whose leaves are the equidistant hypersurfaces above this latter subset. With a suitable renormalization which is closely related to the anisotropic nature of the ambient geometry, the above mentioned geometric objects converge near infinity, inducing the claimed structure on the boundary at infinity.

Place, publisher, year, edition, pages
Springer Nature , 2024. Vol. 307, no 1, article id 8
Keywords [en]
53C21, 53C35, 53C55, 58J60, Asymptotic geometry, Asymptotically symmetric space, Complex hyperbolic space, CR structure
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-345754DOI: 10.1007/s00209-024-03473-0ISI: 001199727200002Scopus ID: 2-s2.0-85189889572OAI: oai:DiVA.org:kth-345754DiVA, id: diva2:1852530
Note

QC 20240418

Available from: 2024-04-18 Created: 2024-04-18 Last updated: 2024-04-26Bibliographically approved

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Pinoy, Alan

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